If \(M=\left[\begin{array}{c}2 \\ -1 \\ 3\end{array}\right]\) and \(N=\left[\begin{array}{lll}7 & 1 & -4\end{array}\right]\), then \((M N)^T\) will be equal to:

The minimum value of \(a x+b y\), where \(x y=c^2\) and \(a, b, c\) are positive, is:

If \(A =\left(\begin{array}{cc}2 & 3 \\ 5 & -2\end{array}\right)\), be such that \(A ^{-1}=K A\), then the value of \(K\) is :

The relation R on the set of real numbers defined by \(R=\left\{(a, b): a \leq b^2\right\}\) is
(A) Reflexive
(B) Not symmetric
(C) Neither reflexive nor transitive
(D) Transitive
Choose the correct answer from the options given below:

'A' speaks the truth in 80% of the cases while 'B' in 90% of the cases. The probability that they contradict each other in stating the same statement is

The sum of order and degree of the differential equation \(\left(x^2 \frac{d^2 y}{d x^2}\right)^{\frac{3}{4}}=5\left(\frac{d y}{d x}\right)^2-3\) is equal to :

If \(\left|\begin{array}{ccc}-1 & 1 & 0 \\ a & b & 1 \\ 1 & 2 & 1\end{array}\right|\) is a singular matrix, then the relation between a and b is:

The method of producing thousands of plants through tissue culture is called as:

The maximum and minimum amplitudes of a modulated carrier wave are 1000 mV and 200 mV respectively, the modulation index is

The corner points of a bounded feasible region determined by the following system of linear inequalities \(x+3 y \leq 60, x+y \geq 10, x \leq y, x \geq 0, y \geq 0\) are \((0,10),(5,5),(15,15)\) and (0,20). Let \(z=2 p x+q y, p, q>0\). If maximum of z occurs at both (15, 15) and (0, 20), then the relation between p and q is

Which of the following has the highest molar conductivity?

When temperature of a ferromagnetic material is increased by 20%, what is the percentage change in it's magnetic susceptibility?

Read the passage carefully and answer the questions based on the passage:
Alcohols are versatile compounds as they can act as both nucleophile and electrophile. They undergo reactions based on cleavage of O-H and C-O bonds. The cleavage of O-H bond reflects the acidic character of alcohols. However they are weaker acids than water, phenol and carboxylic acids. Alkoxide ion formed by loss of proton from the OH group of alcohols reacts with water to form the corresponding conjugate acid - base pair. They act as Bronsted base due to presence of unshared electron pairs on oxygen.Both alcohols and phenol react with carboxylic acids, acid chlorides and anhydrides to form esters. The introduction of acetyl group in alcohols or phenol is known as acetylation. Alcohols react with hydrogen halides to form alkyl halides which form the basis of Lucas test. They also undergo acid catalyzed dehydration to form alkenes. Alcohols can be easily oxidized with variety of oxidizing agents. The nature of the product depends on the type of oxidizing agent and the nature of alcohol.
Which of the following gives the correct sequential steps for dehydration of alcohol?